Using Kirchhoff's laws for multiple batteries and resistors

In summary, the conversation revolved around a circuit question and the correct setup to find the current in the 3rd wire. The person had initially attempted the question and received feedback on the depiction of the "mid-point" connections. After making adjustments, it was confirmed that the equations were correct and the final circuit diagram was approved.
  • #1
Bolter
262
31
Homework Statement
See full question below
Relevant Equations
Kirchhoff 1st and 2nd law
Hey everyone!

Had an attempt at this circuit question, but wanted to check if I got the set up right in order to find the current in the 3rd wire?
Screenshot 2020-04-21 at 12.55.10.png


Here is what I have done
IMG_4655 2.JPG


Thanks!
 
Physics news on Phys.org
  • #2
You have done well, showing the internal resistance in each battery as an explicit external resistor in series.

However, there is a problem with the depiction of the "mid-point" connections. The three ohm wire connects at the midpoints of the two ohm and the four ohm wires. It would be best to split the two ohm "resistor" at its midpoint and to do the same for the four ohm "resistor".

Because the drawing is misleading, the equations you constructed from it are not correct.
 
Last edited:
  • Like
Likes Bolter
  • #3
jbriggs444 said:
You have done well, showing the internal resistance in each battery as an explicit external resistor in series.

However, there is a problem with the depiction of the "mid-point" connections. The three ohm wire connects at the midpoints of the two ohm and the four ohm wires. It would be best to split the two ohm "resistor" at its midpoint and to do the same for the four ohm "resistor".

Because the drawing is misleading, the equations you constructed from it are not correct.

So would this be a much preferred circuit diagram then?

IMG_4659.JPG


I think my loop equations will be the same as before if I use Kirchhoff's law on left & right loop
 
  • Like
Likes jbriggs444
  • #4
Very nice drawing. And now that I look again your equations were correct to start with.
 
  • Like
Likes Bolter

FAQ: Using Kirchhoff's laws for multiple batteries and resistors

1. How do I apply Kirchhoff's laws to a circuit with multiple batteries and resistors?

Kirchhoff's laws are used to analyze the flow of current and voltage in a circuit. For a circuit with multiple batteries and resistors, you can use Kirchhoff's loop rule and junction rule to determine the current and voltage at different points in the circuit. The loop rule states that the sum of the voltage drops around a closed loop in a circuit must equal the sum of the voltage sources. The junction rule states that the sum of the currents entering a junction must equal the sum of the currents leaving the junction.

2. Can Kirchhoff's laws be applied to any type of circuit?

Yes, Kirchhoff's laws can be applied to any type of circuit, including circuits with multiple batteries and resistors. These laws are fundamental principles in circuit analysis and can be used to analyze both simple and complex circuits.

3. How do I handle multiple batteries in a circuit when using Kirchhoff's laws?

When applying Kirchhoff's laws to a circuit with multiple batteries, you must consider the direction of current flow in each loop. The voltage drop across a battery depends on the direction of current flow, so you may need to use the negative value of the battery's voltage if the current is flowing in the opposite direction.

4. Are there any limitations to using Kirchhoff's laws for multiple batteries and resistors?

Kirchhoff's laws are based on the principles of conservation of energy and charge, so they are valid for all circuits. However, they may become more complex to apply in circuits with a large number of components, and they may not be as accurate for circuits with high frequency AC signals or non-linear components.

5. How can I verify the accuracy of my calculations when using Kirchhoff's laws?

You can verify the accuracy of your calculations by using a multimeter to measure the voltage and current at different points in the circuit. The measured values should match the values calculated using Kirchhoff's laws. Additionally, you can use simulation software to model the circuit and compare the results to your calculations.

Similar threads

Kirchhoff's law: Circuit problem with multiple batteries and resistors
Replies
5
Views
2K
Why do the headlights on the car become dim when the car is starting?
Replies
4
Views
893
Circuit with resistor, switch and capacitor
2
Replies
62
Views
4K
How to solve this chain with Kirchhoff's laws?
Replies
18
Views
2K
Grounded circuit, 2 batteries and 2 resistors
Replies
6
Views
2K
Analyzing a circuit with multiple batteries
Replies
15
Views
1K
Current in a resistor with Kirchhoff's laws
Replies
8
Views
1K
Solve Kirchhoff's Laws Homework: Find Current I in a Circuit
Replies
2
Views
1K
Using Kirchhoff's Rule - Theory question
Replies
8
Views
1K
What is the voltage across battery terminals?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top